NCERT Class 12 Physics Chapter 8 Notes Electromagnetic Waves - Download PDF

NCERT Notes for Class 12 Chapter 8: Download PDF

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NCERT Notes for Class 12 Chapter 8 Electromagnetic Waves

The NCERT Notes of Electromagnetic Waves provide students with a fundamental understanding of the topic in easy-to-understand language. These notes will enhance your learning and help you prepare well for your exams.

Displacement Current

"Displacement current is a current which is produced due to the rate of change of electric flux with respect to time". Displacement current is given by

$I_d=\varepsilon_0 \frac{d}{d t}\left(\phi_E\right)$

Maxwell’s Equations

Maxwell put together the basic laws of electricity and magnetism is that, Gauss’ law of electricity, Gauss’ law of magnetism, Faraday’s law of electromagnetic induction, and Ampere- Maxwell’s Circuital law in the form of four fundamental equations, known as Maxwell’s equations.

On the basis of these equations, Maxwell anticipated the existence of electromagnetic waves.

1. Gauss’ law of electricity:- It states that the electric flux through any closed surface is equal to the 1/?₀ times the net charge enclosed by the surface.
   $\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}$
   This equation is called Maxwell’s first equation. This equation is true for both moving and stationary charges.

2. Gauss’s law of magnetism:- It states that the magnetic flux through any closed surface is zero.
   $\oint \vec{B} \cdot d \vec{S}=0$
   This equation is called Maxwell’s second equation. It signifies that free magnetic poles do not exist. This equation also signifies that magnetic lines of force cannot start from a point nor end at a point, that is they are closed curves.

3. Faraday’s laws of Electromagnetic induction:- It asserts that the negative rate of change of magnetic flux across a circuit is equal to the induced emf set up in the circuit.
   $e=-\frac{d \phi_B}{d t}$
   Since emf can be defined as the line integral of the electric field, the above relation can be expressed as
   $\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}$
   The line integral of the electric field along a closed channel is therefore equal to the rate of change of magnetic flux through the surface bounded by that closed path, according to the law.
   This equation is called Maxwell's third equation. It signifies that the electric field is produced by a changing magnetic field.

4. Ampere-Maxwell’s Circuital law:- It states that the line integral of the magnetic field along a closed is equal to μ₀ times the total current linked with the surface bounded by that closed path.

   $
   \oint \vec{B} \cdot d \vec{l}=\mu_0\left(i+i_d\right)
   $
   Where $i_d=\epsilon_0 A \frac{d E}{d t}$

This equation is known as Maxwell’s fourth equation. It signifies that a conduction current, as well as a changing electric field, produces a magnetic field.

Electromagnetic Waves

Sources of electromagnetic waves

"The waves that are produced by accelerated charged particles and composed of electric and magnetic field vibrating transversely and sinusoidally perpendicular to each other and to the direction of propagation are called electromagnetic waves or electromagnetic radiations."

These waves are produced in the following physical phenomena :
(i) An electric charge at rest produces only electrostatic field around it.
(ii) A charge moving with uniform velocity (i.e. steady current) produces both electric and magnetic field, here magnetic field does not change with time hence it does not produce time varying electric field.
(iii) An accelerating charge produces both electric field and magnetic field which varies with space and time which forms electromagnetic wave.
(iv) An accelerating charge (in case of LC oscillation) emits an electromagnetic wave of same frequency as frequency of accelerating charge (i.e., frequency of oscillating LC circuit)
(v) An electron orbiting around its nucleus in a stationary orbit does not emit electromagnetic wave. It will emit only during transition from higher energy orbit to lower energy orbit.
(vi) Electromagnetic wave ( $X$-ray) is produced when high-speed electron enters into target of high atomic weight.
(vii) Electromagnetic wave ( $\gamma$-rays) is produced during the de-excitation of the nucleus in radioactivity.

Nature of electromagnetic waves

(i) It is produced by accelerated charge (e.g., X-ray) and oscillating charge (e.g., LC oscillation).
(ii) It travels in free space with speed equal to $3 \times 10^8 \mathrm{~m} / \mathrm{s}$ which is given by $c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$.
(iii) These waves do not require material medium for their propagation.
(iv) In these waves $\vec{E}$ and $\vec{B}$ vary sinusoidally. $\vec{E}$ and $\vec{B}$ become maximum at same place and at the same time, but perpendicular to each other as well as to direction of propagation. Therefore the phase difference between the two fields is zero. The amplitude of electric and magnetic fields are related to each other as $c=\frac{E_0}{B_0}$. The direction of propagation can be determined by $\vec{E} \times \vec{B}$.

(v) The velocity of electromagnetic wave in a medium is decided by electric and magnetic properties of medium not by the amplitude of electric and magnetic field vector.

The speed of electromagnetic wave in a medium is $v=\frac{1}{\sqrt{\mu \varepsilon}}$.
(vi) The energy carried by electromagnetic wave is equally divided between electric field and magnetic field. Total average energy density $U=\frac{1}{2} \varepsilon_0 E_0^2=\frac{1}{2} \frac{B_0^2}{\mu_0}$.
(vii) Electric field vector of an electromagnetic wave produces optical effect hence it is also known as light vector.
(viii) Electromagnetic wave is not deflected by electric field as well as magnetic field because it consists of uncharged particles called photon.
(ix) Intensity of electromagnetic wave is defined as "energy crossing per second per unit area perpendicular to direction of propagation of electromagnetic wave."

Average intensity is given by
$I=\frac{1}{2} \varepsilon_0 E_0^2 c$ or $\varepsilon_0 E_{\text {r.m.s. }}^2 c$ (in terms of electric field)
$I=\frac{1}{2} \frac{B_0^2}{\mu_0} c=\frac{B_{\mathrm{rms}}^2}{\mu_0} \times c$ (in terms of magnetic field)

Relation Between Magnitudes of Vector E and Vector B in Free Space

Let a sinusoidal electromagnetic wave is propagating in free space along with the positive directions o the X-axis with wave no. k and angular frequency ?. Then, the magnitudes of vector E and vector B acting along Y- and Z-axis, respectively, vary with x and t and can be written as

$\begin{array}{ll}E=E_0 \sin (\omega t-k x) & \ldots \ldots(i) \\ B=B_0 \sin (\omega t-k x) & \ldots \ldots(i i)\end{array}$

Where E₀ and B₀ are the maximum values of E and B, respectively.

$k=\frac{2 \pi}{\lambda}, \omega=2 \pi v$

Here λ is the wavelength and v is the frequency of the wave.

$\therefore \frac{\omega}{k}=\frac{2 \pi v}{2 \pi / \lambda}=v \lambda=c$

c is the speed of the electromagnetic wave which is the speed of light in free space. From eqn (i),

$\frac{\partial E}{\partial x}=-k x \cos (\omega t-k x)$

From eqn (ii),

$\frac{\partial B}{\partial t}=\omega B_0 \cos (\omega t-k x)$

Putting these values in this relation

$\frac{\partial \vec{E}}{\partial x}=-\frac{\partial \vec{B}}{\partial t}$

we get

$\begin{aligned} & k x \cos (\omega t-k x)=\omega B_0 \cos (\omega t-k x) \\ & \frac{E_0}{B_0}=\frac{\omega}{k}=c\end{aligned}$

Since E and B are in the same phase.

$\frac{E}{B}=c$

At any point in space. Thus, the ratio of the magnitude of electric field and magnetic field equals the speed of light in free space.

Energy Density in Electromagnetic Waves

The energy density in an electric field E in a vacuum is ϵ₀E²/2, and that in a magnetic field B is B²/2μ₀. Thus, the energy density is associated with an electromagnetic wave is

$
u=\frac{1}{2} \epsilon_0 E^2+\frac{1}{2} \frac{B^2}{\mu_0}
$

An electromagnetic wave propagating along the X-axis and the magnitude of vector E and vector B, acting along the Y- and Z- axis respectively can be written as

$E=E_0 \sin (\omega t-k x)$ and $B=B_0 \sin (\omega t-k x)$

Where E₀ and B₀ are the maximum values of E and B respectively. Putting these values in eqn (i), we get

$u=\frac{1}{2} \epsilon_0 E_0^2 \sin ^2(\omega t-k x)+\frac{1}{2} \frac{B_0^2}{\mu_0} \sin ^2(\omega t-k x)$

The time average of sin² over any whole number of cycles is ½. Therefore the average energy density of an e.m. wave is

$\bar{u}=\frac{1}{2} \epsilon_0 E_0^2+\frac{1}{2} \frac{B_0^2}{\mu_0}$

Here ϵ₀E²/2 is the average kinetic energy density u_e and B²/2μ₀ is the average magnetic density u_m.

Electromagnetic Spectrum

Maxwell predicted the existence of electromagnetic wave.
Electromagnetic wave experimentally discovered by Hertz.
At the end of nineteenth century, visible light, ultraviolet, infrared, X-rays and $\gamma$-rays had also been discovered. We now know that electromagnetic waves include (i) $\gamma$-rays (ii) $X$-ray (iii) ultraviolet rays (iv) visible light ( $\mathbf{v}$ ) infrared (vi) microwaves (vii) radiowaves.
"The orderly distribution of electromagnetic radiations according to their frequency (or wavelength) is called electromagnetic spectrum".

(i) Radio waves

• It is produced by the accelerated motion of charges in conducting wires. (i.e., by oscillating electric circuit).
• Its frequency range is 500 kHz to about 1000 MHz
• Its wavelength range is $\approx 10^{-2} \mathrm{~m}$ to $10^4 \mathrm{~m}$.
• They are reflected, refracted and diffracted, used in radio and T.V. communication.

(ii) Microwaves

• It is produced by special vacuum tubes (called Klystrons, Magnetrons and Gunn diodes)
• Its frequency range is $\approx 1 \mathrm{GHz}$ to 300 GHz
• Uses:
  (a) It is used in radar system for aircraft navigation.
  (b) It is used to detect speed of tennis ball, cricket ball, automobile.
  (c) It is used in microwave ovens.

(iii) Infrared Waves

• It is produced by hot bodies i.e. vibrations of atoms and molecules. (Hence also called heat waves).
• It is not detected by human eye but snake can detect it.
• These waves are readily absorbed by water, $\mathrm{CO}_2, \mathrm{NH}_3$ etc.
• Its frequency range is $10^{11} \mathrm{~Hz}$ to $10^{14} \mathrm{~Hz}$.
• Its wavelength lies between $1 \mathrm{~mm}-700 \mathrm{~nm}$.
• It is detected by thermopiles, bolometer, infrared photographic film.
• Uses:
  (a) Infrared lamp is used in physical therapy i.e. to treat muscular strain.
  (b) It is responsible for keeping average temperature through green-house effect.
  (c) Infrared detectors are used in earth satellite, both for military purposes and to observe growth of crops.

(iv) Visible Light

• It is a narrow range of electromagnetic spectrum
• It is produced by atomic excitation
• Its frequency range from $4 \times 10^{14} \mathrm{~Hz}$ to about $7 \times 10^{14} \mathrm{~Hz}$
• Its wavelength lies between 700 nm to 400 nm
• The visible light emitted or reflected from the objects around us provides us information about the world.
• It is detected by the eyes, photocells, photographic film.

(v) Ultraviolet Rays

• It is produced by sun, special lamps and very hot bodies.
• Its frequency lies between $8 \times 10^{14} \mathrm{~Hz}$ to $5 \times 10^{16} \mathrm{~Hz}$.
• Its wavelength lies between 400 nm to 0.6 nm .
• It is detected by photocells, photographic film.
• Most of the ultraviolet radiations coming from the sun are absorbed by the ozone layer in the earth's atmosphere.
• The UV rays in large quantity produce harmful effect on human being, it causes production of melanin, tanning of the skin.
• It is absorbed by the ordinary glass.
• Uses:
  (a) Due to its short wavelength it can be focussed into very narrow beam which is used for high precision applications e.g., LASIK (laser assisted in situ keratomileusis) eye surgery.
  (b) UV lamps are used to kill germs in water purifiers.
  (c) To destroy the bacteria and for sterilizing the surgical instruments.
  (d) In finger print technology.

(vi) X-rays

• Its frequency order is $10^{16} \mathrm{~Hz}$ to $10^{21} \mathrm{~Hz}$.
• Its wavelength lies between 10 nm to $10^{-4} \mathrm{~nm}$.
• It is produced in a tube called modern X-ray tube.
• It is detected by photographic film, Geiger tubes and ionisation chamber.
• X-ray are used as a diagnostic tool in medicine and as a treatment for certain forms of cancer.
• In engineering it is used for detecting faults, cracks, flaws and holes.
• It is used for detecting pearls in oysters, defect in rubber tyres, golds.

(vii) Gamma rays

• It is high frequency radiation which is produced in nuclear reactions they are emitted by radioactive nuclei.
• Its frequency range is $10^{18} \mathrm{~Hz}-10^{22} \mathrm{~Hz}$.
• Its wavelength is $<10^{-3} \mathrm{~nm}$. From about $10^{-10} \mathrm{~m}$ to less than $10^{-14} \mathrm{~m}$.
• It is detected by photographic film, Geiger tubes, ionisation chamber.
• They show phosphorescence, fluorescence, polarisation, diffraction.
• They have very high penetrating power.
• They are used for cancer therapy.
• They provide important information regarding nuclear structure.

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